How important is wisdom for wizards? The description says "it is for druids and other classes", but I wonder why is not for wizards? Should I ignore it, and don't put any point into wisdom when I choose wizard class, or does it have some effect? If yes what effect it has?

Wizards are based on intelligence for casting spells, not wisdom.

You can put wisdom at 10 when making a wizard so as to not have any negative stats as wisdom is used for making saving throws versus will, which applies to mind-affecting spells. Wisdom is needed to read the dreams of the sleeping man in Hordes of the Underdark, but the amount that you'd need to sink into wisdom to do that is just not going to be worth it as a wizard.

Play enough modules (including official ones) and you'll figure out fast that you don't go to wizards for wisdom. They're always doing crazy things like making clones of themselves and forgetting which one is their original self.

Fun fact, as far as DnD goes in general, wizards would also use Wisdom for the Wish spell.

Low Wisdom casters are great fun for the DM where the wish spell is involved!